In this appendix we calculate which effective blockade strength can be achieved when using Caesium atoms, \(\mathinner {|{r}\rangle } = \mathinner {|{107 p_{3/2}\, m =3/2}\rangle }\)  and \(\mathinner {|{1}\rangle }=\mathinner {|{6S_{1/2}F=4\, m_F=4}\rangle }\) , and aligning the atoms perpendicular to quantization axis. This is the same setup as assumed in [1]}, [2]}. The interaction between two atoms at a distance \(R\)  is given by the dipole-dipole potential
\(V_{dd} = \frac{e^2}{4\pi \epsilon _0}\frac{\hat{x}_1\cdot \hat{x_2} - 3(\hat{x}_1\cdot \vec{n})(\hat{x}_2\cdot \vec{n})}{R^3}\) 
